Abstract In this work we consider model-based optimization of polymer flooding. The reservoir performance is optimized by finding for each injection well optimal values for control variables such as injection and production rates, polymer concentrations, and times when to switch from polymer to water injection (i.e. polymer grading). The same technique can also be applied to optimize other EOR processes such as for example designer water flooding, alkali-surfactant polymer (ASP) flooding and foam flooding. The optimization method that has been used relies on the adjoint implementation in our in-house reservoir simulator to efficiently calculate the gradients. The adjoint method enables the computation of gradients with respect to injection and production rates, injection compositions of each well and switching times of each well at the additional cost of approximately the computation time of a single reservoir simulation. The optimization method uses the adjoint-based gradients to estimate the values of all polymer injection control variables that maximize reservoir performance.

The optimization method is demonstrated on a full-field reservoir simulation model. The physics that is modeled includes polymer mixing, hydrodynamic acceleration of the polymer molecules and adsorption of the polymer to the rock. The example shows that the Net Present Value increases significantly as a result of the optimization, mainly due to increased oil production and decreased polymer injection. The obtained optimal control is physically interpreted, so that the learning points from the model-based optimization can be applied to the field and can be used to enhance the polymer flood.

Introduction The recovery factor of a hydrocarbon reservoir can be significantly increased if water is injected into the reservoir to displace the hydrocarbon towards the producing wells. For hydrocarbon reservoirs with an unfavorable mobility ratio (i.e. the mobility of the displacing fluids is higher than the mobility of the to-be-displaced fluids), the flooding efficiency can be increased by injecting a mixture of polymer and water. As a result the viscosity of the displacing fluids increases, the mobility ratio becomes more favorable and the recovery factor increases.

Polymer flooding has been applied already several decades to a significant number of fields; see Kumar 2008 for an evaluation of published field data. The Daqing field is a convincing example for which polymer flooding, combined with improved well and reservoir management, increased the oil recovery with 15% (Shao et al, 2008). With favorable oil prices and modest polymer prices (polymer is used extensively in e.g. the food industry), polymer flooding becomes increasingly interesting for oil companies. Once a reservoir is found to be a suitable candidate for polymer flooding, design variables such as polymer type, polymer slug size, polymer concentrations and injection and production rates are candidates for optimization. In this work the focus is on optimization of the polymer flooding process. This requires a model of the reservoir field that has been properly matched to all historical measurements and is believed to give reliable predictions. This is only possible if the reservoir simulator is capable to model the relevant polymer dynamics. Also note that once the polymer flooding has been designed, it is important to monitor the polymer flooding process. Examples hereof are monitoring fracturing around the injector wells and monitoring the actual viscosity of the displacing fluid. Other work on optimization of the polymer flooding process is reported in • Ramirez (1984): applying adjoint-based sensitivities for polymer and ASP optimization on 1D and 2D reservoir models. • Clemens et al. (2010): applying streamline-based sensitivities for polymer optimization. • Zhang et al. (2005) and Mantilla & Srinivasan (2011): applying Experimental Design to generate polynomial proxy models that are used for the purpose of polymer flooding optimization.

Note that Chen et al. (2008) use Ensemble Kalman Filtering (EnKF) for water flood optimization, but naturally the EnKF can also be applied for optimization in the area of EOR, as has been done by Odi et al. (2010).

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